Go ahead. Make our day. Try some seriously secure messaging by Threema.com.
With Threema’s true end-to-end encryption, you can rest assured that only you and the intended recipient can read your messages. Unlike other popular messaging apps (including those claiming to use encryption), even the server operators and tech people at Threema have absolutely no way to read your messages. There’s no charge per message, but the in-app cost of buying Threema will guarantee Threema’s long-term viability and keep YOU as the customer (rather than some kind of advertising dollars later. (Thanks to Greg for the heads-up on this.)